Susceptibility near a critical point. Consider a ferromagnetic system with n spins per volume, where each spin has magnetic moment u. There is an effective B-field from the mean magnetization, BE = AM. However, now there is an external field, Bo, such that the total effective field is B = AM + Bo. (a) Assume B0 = 0 (no external field). Near the critical point, the magnetization will have the form M x t- telP. Calculate te and B. (b) The magnetic susceptibility x = dM/dB near the critical point will obey x x (t-T.)". When t >T, M and B are both very small, so x = M/B also works. Calculate y.
Susceptibility near a critical point. Consider a ferromagnetic system with n spins per volume, where each spin has magnetic moment u. There is an effective B-field from the mean magnetization, BE = AM. However, now there is an external field, Bo, such that the total effective field is B = AM + Bo. (a) Assume B0 = 0 (no external field). Near the critical point, the magnetization will have the form M x t- telP. Calculate te and B. (b) The magnetic susceptibility x = dM/dB near the critical point will obey x x (t-T.)". When t >T, M and B are both very small, so x = M/B also works. Calculate y.
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![Susceptibility near a critical point. Consider a ferromagnetic system withn spins per volume,
where each spin has magnetic moment u. There is an effective B-field from the mean
magnetization, BĘ = AM. However, now there is an external field, Bo, such that the total effective
field is B = AM + Bo.
(a) Assume Bo = 0 (no external field). Near the critical point, the magnetization will have the
form M c |t- tel. Calculate t, and ß.
(b) The magnetic susceptibility x = dM/dB near the critical point will obey x x (t -T)".
When t > T, M and Bare both very small, so x = M/B also works. Calculate y.
(c) Sketch or plot M from part (a) and x from part (b) on the same axes, both as a
function of t/t.. Make sure you only plot x for t/t, > 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98247bf2-b28c-4fb1-bda9-6231195909b3%2F2fdaaa2a-0477-496e-b395-63559f121d05%2Fp690s0m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Susceptibility near a critical point. Consider a ferromagnetic system withn spins per volume,
where each spin has magnetic moment u. There is an effective B-field from the mean
magnetization, BĘ = AM. However, now there is an external field, Bo, such that the total effective
field is B = AM + Bo.
(a) Assume Bo = 0 (no external field). Near the critical point, the magnetization will have the
form M c |t- tel. Calculate t, and ß.
(b) The magnetic susceptibility x = dM/dB near the critical point will obey x x (t -T)".
When t > T, M and Bare both very small, so x = M/B also works. Calculate y.
(c) Sketch or plot M from part (a) and x from part (b) on the same axes, both as a
function of t/t.. Make sure you only plot x for t/t, > 1.
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